# Bayesian sequential design of computer experiments for quantile set inversion

arXiv: https://arxiv.org/abs/2211.01008 · HTML: https://mlsanity.com/paper/2211.01008/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [A supermartingale approach to Gaussian process based sequential design of experiments](https://mlsanity.com/paper/1608.01118/) (2016)
- [Adaptive Design of Experiments for Conservative Estimation of Excursion Sets](https://mlsanity.com/paper/1611.07256/) (2016)
- [Contour location via entropy reduction leveraging multiple information sources](https://mlsanity.com/paper/1805.07489/) (2018)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [The ICSCREAM methodology: Identification of penalizing configurations in computer experiments using screening and metamodel -- Applications in thermal-hydraulics](https://mlsanity.com/paper/2004.04663/) (2020)

## Built on by (most cited first, 2 of 2)

- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)
- [Bayesian Active Learning of (small) Quantile Sets through Expected Estimator Modification](https://mlsanity.com/paper/2506.13211/) (2025)

## Abstract (arXiv)

We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem we propose a Bayesian strategy, based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.